
A Solution of the P versus NP Problem based on specific property of clique function
Circuit lower bounds are important since it is believed that a superpol...
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On the complexity of detecting hazards
Detecting and eliminating logic hazards in Boolean circuits is a fundame...
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Lifting with Simple Gadgets and Applications to Circuit and Proof Complexity
We significantly strengthen and generalize the theorem lifting Nullstell...
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Optimal ShortCircuit Resilient Formulas
We consider faulttolerant boolean formulas in which the output of a fau...
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On the relation between structured dDNNFs and SDDs
Structured dDNNFs and SDDs are restricted negation normal form circuits...
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On Lev Gordeev's "On P Versus NP"
In the paper "On P versus NP," Lev Gordeev attempts to extend the method...
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Local negative circuits and cyclic attractors in Boolean networks with at most five components
We consider the following question on the relationship between the asymp...
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On P Versus NP
I generalize a wellknown result that P = NP fails for monotone polynomial circuits  more precisely, that the clique problem CLIQUE(k^4,k) is not solvable by Boolean (AND,OR)circuits of the size polynomial in k. In the other words, there is no Boolean (AND,OR)formula F expressing that a given graph with k^4 vertices contains a clique of k elements, provided that the circuit length of F, cl(F), is polynomial in k. In fact, for any solution F in question, cl(F) must be exponential in k. Moreover this holds also for DeMorgan normal (abbr.: DMN) (AND,OR)formulas F that allow negated variables. Based on the latter observation I consider an arbitrary (AND,OR,NOT)formula F and recall that standard NOTconversions to DMN at most double its circuit length. Hence for any Boolean solution F of CLIQUE(k^4,k), cl(F) is exponential in k. I conclude that CLIQUE(k^4,k) is not solvable by polynomialsize Boolean circuits, and hence P is not NP. The entire proof is formalizable by standard methods in the exponential function arithmetic EFA.
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